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Further results on consensus formation in the Deffuant model

Journal article
Authors Olle Häggström
Timo Hirscher
Published in Electronic Journal of Probability
Volume 19
Pages artikel nr 19
ISSN 1083-6489
Publication year 2014
Published at Department of Mathematical Sciences
Department of Mathematical Sciences, Mathematical Statistics
Pages artikel nr 19
Language en
Keywords Deffuant model; consensus formation; percolation.
Subject categories Probability Theory and Statistics


The so-called Deffuant model describes a pattern for social interaction, in which two neighboring individuals randomly meet and share their opinions on a certain topic, if their discrepancy is not beyond a given threshold θ. The major focus of the analyses, both theoretical and based on simulations, lies on whether these single interactions lead to a global consensus in the long run or not. First, we generalize a result of Lanchier for the Deffuant model on Z, determining the critical value for θ at which a phase transition of the long term behavior takes place, to other distributions of the initial opinions than i.i.d. uniform on [0,1]. Then we shed light on the situations where the underlying line graph Z is replaced by higher-dimensional lattices Z^d, d≥2, or the infinite cluster of supercritical i.i.d. bond percolation on these lattices.

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